Constructions of quantum caps in projective space PG(r, 4) by recursive methods and computer search are discussed. For each even n satisfying $$n\ge 282$$ n ≥ 282 and each odd z satisfying $$z\ge 275$$ z ≥ 275 , a quantum n-cap and a quantum z-cap in $$PG(k-1, 4)$$ P G ( k - 1 , 4 ) with suitable k are constructed, and $$[[n,n-2k,4]]$$ [ [ n , n - 2 k , 4 ] ] and $$[[z,z-2k,4]]$$ [ [ z , z - 2 k , 4 ] ] quantum codes are derived from the constructed quantum n-cap and z-cap, respectively. For $$n\ge 282$$ n ≥ 282 and $$n\ne 286$$ n ≠ 286 , 756 and 5040, or $$z\ge 275$$ z ≥ 275 , the results on the sizes of quantum caps and quantum codes are new, and all the obtained quantum codes are optimal codes according to the quantum Hamming bound. While constructing quantum caps, we also obtain many large caps in PG(r, 4) for $$r\ge 11$$ r ≥ 11 . These results concerning large caps provide improved lower bounds on the maximal sizes of caps in PG(r, 4) for $$r\ge 11$$ r ≥ 11 .
Quantum Information Processing – Springer Journals
Published: Dec 11, 2015
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera